Evaluate. $\dfrac{2^{^{\scriptsize -\dfrac{4}{3}}}}{54^{^{\scriptsize -\dfrac{4}{3}}}}=$
$\begin{aligned} \dfrac{2^{^{\scriptsize -\dfrac{4}{3}}}}{54^{^{\scriptsize -\dfrac{4}{3}}}}&=\left(\dfrac{2}{54}\right)^{^{\scriptsize -\dfrac43}} \\\\ &=\left(\dfrac{1}{27}\right)^{^{\scriptsize -\dfrac43}} \\\\ &=27^{^{\scriptsize\dfrac43}} \\\\ &=\left(\sqrt[3]{27}\right)^4 \\\\ &=3^4 \\\\ &=81 \end{aligned}$ In conclusion, $\dfrac{2^{^{\scriptsize -\dfrac{4}{3}}}}{54^{^{\scriptsize -\dfrac{4}{3}}}}=81$